Algebraic Geometry Seminar: "Classes of compactified Jacobians in the Grothendieck ring"

Organizer: Matt Kerr

Host: Roya Beheshti

Abstract: Let $C$ be a {\em nodal curve} over and algebraically closed field $k$.  Denote with $\Pic^0(C)$ the {\em generalized} Jacobian of $C$, which is the classifying space for line bundles on $C$ having degree zero on each irreducible component. If the dual graph of $C$ is not a tree, then $\Pic^0(C)$ is not compact. But (many) nice compactifications of $\Pic^0(C)$ are known. I will describe how one can use the combinatorics of the dual graph to compute the class of these compactifications in the "Grothendieck ring of $k$-varieties''. This is ongoing joint work with Alberto Bellardini. The talk should be accessible to graduate students.